Gear



Patented July 28, 1936 Um'rl-:D STATES GEAR. Nelson De Long, Chicago, Ill., assignor to Arthur Dean, trustee, Chicago, Ill.

Application July 5, 1932, Serial No. 620,789.

4 Claims. (Cl. 'X4-416) My invention relates to toothed gears, and has for its object the production of a form of tooth which will have great efciency and will be noiseless, and one which is easy of production and will be stronger than other teeth of the samenominal dimensions.

In the making of ordinary gears it has been the practice heretofore to adopt for the tooth ank a curve which will give the best possible results in plain spur gearing. I have departed from that practice and have adopted a curve which is unsatisfactory for plain spur gears, but which, when combined with the helix of helical gears, gives perfect and continuous rolling contact at the pitch lines.

The curve I use for the flanks of the gear teeth is known as the equiangular or logarithmic spiral. This is a curve in which the tangent to any point on the curve makes the same angle with the radius vector of that point as does the tangent of any other point to its radius Vector. I may use a curve which cuts radii at any angle, but for illustration I use a curve which cuts radii at thirty degrees, which is a convenient angle and one well adapted for gear teeth of all sizes.

Two gears having teeth with flanks formed by the same spiral will have those flanks in pointy contact only in the straight line between gear centers. To maintain the points of contact uniformly at the pitch line, and on the line between gear centers, I make use of the wellknown helical type of'J gear.

In the accompanying drawing Fig. 1 represents a gear in mesh with four other gears, together with construction lines showing how the curvesI forming the anks of the teeth are found;

Figs. 2 and 3 are diagrams showing how diierent points in a curve of the same angle meet on l the straight line between centers of gears; and

Fig. 4 is a fragment of two double helical gears, commonly known as herringbone gears.

The gear I0, having'its center at I I, is in mesh with another gear I2 of the same size and with a center at I3. The gear I is also in mesh with an internal gear I4 of twice the diameter of gear I I) and with its center at I5. The gear IIJ also engages a three-toothed gear I 6 having a center at I1, and a rack I8. In this drawing, the gear I0 may be considered as a driver moving in the direction of the arrow I9.

The pitch line of the gear I0 is the line 20, the pitch line of the gear I2 is at 2I, that of gear I4 is at 22, and that of gear I6 as it 23.

The curve which forms the ank of a tooth based upon a spiral of any particular angle. is a short segment of that spiral, and it may be a segment taken at any part of the spiral. When so made, it will work perfectly with another tooth having its flank from the same or any other segment of the spiral.

In Fig. 2, let A-B be a line passing thru the centers of two gears in mesh with each other, and the point P be the point where the pitch lines touch each other. 'like centers of the gears may be at any convenient places on the line AB, but preferably will be on extensions thereof. The line C-D passes thru the point P at an angle to the line A-B which is the angle of the adopted spiral. In the present case this is thirty degrees. The curve 24 having its center atl25, and the curve 26 having its center at 21, are identical curves-being thirty degree logarithmic spirals. The line C-D is tangent to both of them at the point P.

If the curves 24 and 26 are turned about the points 25 and 21 as pivots, and are kept in contact with' each other while being turned, there will be perfect rolling contact at the meeting point, and that. meeting point will travel along the line A-B toward either 25 or 21 according to the direction of turn. And the lineC-D tangent to the two curves at their point of contact will remain uniformly at the same angle, which is represented as thirty degrees in the drawing.

In Fig. 3, we have lines A--B and C-D cutting each other at the point P and at an inclination to eachv other of thirty degrees. The curve 28. having its origin (center) at 29, is identical with the curve having its origin at 3|. 'I'hey are both tangent to the line C-D at the point P. As

far as ythe drawing goes, that part of the curve 30 which lies between 3| and P is simply a. dupli cate of the first part of the curve 28.

Referring to Fig. 1, and taking a tooth 32 of gear I0 where it engages the rack I8, radial lines 33 and 34 are drawn to points on the pitch line .20 which will represent the intended thickness of the tooth at the pitch line. With II as a center, there is drawn al circle 35 which is less than the diameter of the circle 20. The distance vbetween the circle 35 and the circle 20 on any radius from the center II, is the radius vector. of` the curve used in forming the anks of the gear teeth shown. The dotted lines 36 and 31, having their origins at 38 and 39, are those parti of the logarithmic spiral inside of the flanks of the teeth.

The center of the internal gear I4 is at I5. With I5 as a center, draw the arc 40 which is simply a part of a circle having a purpose similar to the purpose of the circle 35. Lay of! on the pitch circle 22 the points 4I and 42 representing the space between two teeth on the gear I4. From 4I and 42 draw lines which pass thru the center I5 and-cut arc 40 at points 43 and 44. The point 43 is the center or origin for the curve 45, and the point 44 is the center for curve 46.

Comparing Fig. l with Fig. 3, the distance on line A-B (Fig. 3) between the point 29 and point P corresponds to the distance between 42 and 43 of Fig. 1. And the distance between 3I and P of Fig. 3 corresponds to the distance between 36 and I5 on the radius 33. As it is diown in Fig. 3 that curves 28 and 30 are tangent in the same way at point P in line C-D, it will be evident that the curve 36 of Fig. 1 has the same tangential contact at point I5 as would occur if the tooth curve were drawn from the center II insteadof from the center 36.

The curves 45 and 46 are the same curves before mentionedthirty degree logarithmic spirals-vbut the part of the curve for tooth flank is further out from the center. In the caseof gear I6, the same principles are involved, but the part of the curve used is the part removed 'only a short distance from the center. A rack is a gear of infinite diameter. As a consequence, the anks of the rack teeth may be straight lines inclined to the face of the rack at the same angle as that adopted for the spiral. In the present case, this is thirty degrees.

When gears I6 and I2 are in the position shown in Fig. l, there is an ideal drive with rolling contact at the pitch line. If these gears are plain spur gears, there will continue, for a time, to be rolling contact on `the line II--I3 joining the .cannot be used for that purpose.

centers of these gears during motion of said gears, but the point of contact will move along line I I--I3 from the driving toward the driven gear.

To maintain the point of contact between driving and driven gears uniformly at the pitch line, I apply this spiral curve to helical gears, or double helical gears known as herringbone gears. When two helical gears operate together, the point of contact on the pitch line, and on a line joining the centers of the shafts, travels along the helix of the gear tooth. By combining the rolling contact of tooth flanks formed on logarithmic spirals, with the helix of helical teeth, I am enabled to keep the contact point always on the pitch line.

It is to be noticed that the logarithmic spiral is an open curve, that is, one which does not repeat itself no matter how far it is extended. It

is a principle of mathematics that a non-repeating curve cannot be used for thetransmission of continuous rotation, and scientific authority has specifically stated that the logarithmic spiral But by combining an enclosed curve with another curve, as the helix, I am enabled to produce continuous rotation and also to substitute rolling contact for sliding contact in gearing.

Fig. 4 represents gears I0 and I2 as herring- ,p a logarithmic spiral.

bone gears. In this construction, the contact points on any double pair of teeth begin at the center line 41 and move outward in each direction to the ends 48. This action eliminates all sliding friction of both approach and recession, 5

and leaves only -rolling friction. The helix used may be of any convenient degree. v From the foregoing description it will be evident that the flanks of the teeth have a shape o! face which is a compound curve. This compound l0 I curved face is a spiral in one direction and a helix in a direction perpendicular thereto, but

f in a bevel gear, the second curve would not neccurve on another of the same angle is the same for all parts of the curve. and consequently for all degrees of curvature. From this fact comes the ability of the curve to maintain contact at the pitch line. Gear teeth of this form may be of a length similar to those of other forms, but are preferably somewhat shorter because vthe working face is limited to a narrow band at the pitch line. Because the rolling action of one contact face on another, as illustrated in'Fig. 2, is .independent of the distance between the centers of the curves, longer teeth permit some variation in distance between centers of gears without impairing the efliciency of operation.

But long .teeth have a tendency for their tips to interfere during operation. 'I'his tendency is reduced by using for gear flanks those parts of the 4 spiral which are near to the origin rather than l those parts which are far out. This is one reason for having the curves begin in a circle 35 rather than at or near the center II. Anotherreason is that it makes possible the use of the same cutter for al1 sizes of gears having the same pitch. What I claim is: v

1. A gear having the faces of its teeth in the form of a compond curve, said compound curve being a logarithmic spiral in one direction and a curve in a direction perpendicular to the spiral.

2. A helical gear havingeach ank of its teeth on a curve which consists of a short segment of 3. A gearhaving each flank of its teeth in the form of a short segment of a logarithmic spiral, the radius vector of the spiral at the pitch line of the gear being less than the radius of the gear.

4. A helical gear having each flank of its teeth 6( on a curve which consists of a segment of a log-` arithmic spiral, the center of which spiral is on a gear radius to the point where the curve cuts the pitch line of the gear.

' NELSON DE LONG. 6: 

